An integrated Large Eddy Simulation (LES) model for soot evolution in turbulent reacting flows is applied to the simulation of an aircraft combustor. The detailed chemical kinetics of fuel oxidation, soot precursor formation, and heat losses due to gas-phase and soot radiation are described with the Radiation Flamelet/Progress Variable (RFPV) model, which has been modified to account for the removal of soot precursors from the gas-phase. The evolution of soot is modeled with the Hybrid Method of Moments (HMOM), a statistical model requiring the solution of only a few transport equations describing the statistics of the soot population. In addition, a novel presumed subfilter PDF approach is used to account for the unresolved small-scale soot-turbulence-chemistry interactions. This integrated model is combined with state-of-the-art unstructured LES technology to simulation soot evolution in the Pratt & Whitney PW6000 aircraft combustor. A Lagrangian approach is used to model the secondary break-up and evaporation of the liquid spray, and the chemistry of Jet-A is described with a three-component surrogate. The combustor is simulated at two different overall fuel-to-air ratios, and the differences in soot dynamics are investigated.